Problem: Solve for $x$. Give an exact answer. $0.5(5-7x) = 8- (4x + 6)$ $x =$
Solution: We need to manipulate the equation to get $x$ by itself. $\begin{aligned} 0.5(5-7x) &= 8- (4x + 6) \\\\ 2.5 -3.5x &= 8 - 4x - 6 ~~~~~~~~~~\gray{\text{Distribute}}\\\\ 2.5-3.5x &= 2-4x ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 2.5-3.5x {+4x} &= 2-4x {+4x} ~~~~~~~~~~\gray{\text{Add 4x to each side}}\\\\ 2.5 +0.5x &= 2 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 2.5 + 0.5x {-2.5}&= 2{-2.5}~~~~~~~~~~\gray{\text{Subtract 2.5 from each side}} \\\\ 0.5x&= -0.5~~~~~~~~~~\gray{\text{Combine like terms}} \\\\ \dfrac{0.5x}{{0.5}}&= \dfrac{-0.5}{{0.5}}~~~~~~~~~~\gray{\text{Divide each side by 0.5}} \\\\ x &= {-1} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $x = {-1}~~~~~~~~$ [Let's check our work!]